Apple Logic Pro 7 - Manual (Page 630)

630 Chapter 21 Song Settings and Preferences
Tuning Settings
A real-time tuning system is available for use with Logic’s software instruments. There
are a number of parameter settings that are accessible via the File > Song Settings >
Tuning panel.
We’ll discuss these options shortly, but before beginning, we’d like to cover some basics
and background information.
About Alternate Tunings
The twelve tone scale that is currently used in Western music is a development that
took centuries. Hidden in-between these twelve notes are a number of other
microtones that represent different mathematical ways of expressing the frequency
intervals between “tones”.
To explain, let’s take a look at the harmonic series, and the underlying harmonic theory.
Imagine that you have a fundamental frequency of 100 Hz (100 vibrations per second),
the first harmonic is double that, or 200 Hz. The second harmonic is found at 300 Hz,
third at 400 Hz, and so on. Musically speaking, we know that when frequency doubles,
pitch increases by exactly one octave. The second harmonic (300 Hz) is exactly one
octave and a pure fifth higher than the fundamental frequency (100 Hz).
From this, you would assume that tuning an instrument so that each fifth is “pure”
would be the way to go, right? In doing so, you would expect a perfectly tuned scale,
as you worked your way from C though to the C above or below. Close, but no cigar.